Boris Johnson has promised to review so-called “sin taxes” to see if they unfairly target those on lower incomes.
The Tory leadership contender wants to examine whether levies on foods high in salt, fat and sugar are effective, and has vowed not to introduce any new ones until the review is complete.
Both leadership candidates were asked at a hustings about a proposed new tax on milkshakes.
It comes as a charity says millions are at risk of cancer due to their weight.
According to Cancer Research UK, obesity now causes more cases of four common cancers in the UK than smoking.
Mr Johnson questioned whether levying these types of taxes disproportionately affected the disadvantaged, and suggested that Brexit would allow the UK to examine its tax policy.
Foreign Secretary Jeremy Hunt said he would rather target manufacturers than taxpayers when it came to less healthy products.
Mr Johnson and Mr Hunt are vying to be the next leader of their party and the next UK prime minister, and have been appearing in a number of events across the UK.
The Conservative Party’s 160,000 members will begin voting for their preferred candidate next week and Theresa May’s successor is expected to be announced on 23 July.
Mr Johnson repeated his opposition to a milkshake tax, saying it would “clobber those who can least afford it”.
“If we want people to lose weight and live healthier lifestyles, we should encourage people to walk, cycle and generally do more exercise,” he said.
“Rather than just taxing people more, we should look at how effective the so-called ‘sin taxes’ really are, and if they actually change behaviour.”
He added: “Once we leave the EU on 31 October, we will have a historic opportunity to change the way politics is done in this country. A good way to start would be basing tax policy on clear evidence.”
Mr Hunt said he would “threaten” manufacturers of milkshakes, or less healthy food and drink, with legislation “if they don’t play ball”.
He added: “But my experience is, if you make that threat, you don’t actually need to follow through with the dreaded milkshake tax.”
Former health minister Steve Brine, who is supporting Mr Hunt, criticised Mr Johnson’s suggestion.
But Treasury Minister Liz Truss, who is supporting Mr Johnson, said “taxes on treats” hit those on the lowest incomes, and people should be “free to choose”.
Tax per litre
The so-called “sugar tax” came into force in April 2018, meaning drinks with more than 8g per 100ml are taxed at 24p per litre, and those containing 5-8g of sugar per 100ml are taxed at 18p per litre.
It was introduced in 2016 by then-Chancellor George Osborne to tackle childhood obesity, while raising £275m for the Treasury.
Pure fruit juices are exempt as they do not carry added sugar, while drinks with a high milk content are currently exempt due to their calcium content.
Camilla Cavendish, who argued for the tax as ex-PM David Cameron’s head of policy, told BBC Radio 4’s Today programme she thought Mr Johnson would be wrong to review it.
She said she had made the case for the levy after becoming concerned about the cost to the NHS of treating diabetes, and obesity rates among poorer children.
“Boris is talking about not clobbering people on lower incomes, but actually I think that tax is one way to help people just drink better,” she said.
She added that drinks manufacturers responded “really well” to the tax change and have altered recipes to lower sugar content as a result.
Cancer Research UK chief executive Michelle Mitchell said such taxes had “a positive effect”.
She said: “They have been highly effective in bringing down smoking rates to record lows, including within deprived communities, and the Treasury’s own analysis showed the tax on sugary drinks took 90 million kg of sugar out of the nation’s diet on day one.
“Physical activity is one way to lose weight, but the government also has a big role to play if we are to significantly reduce obesity levels.”
England’s chief medical officer has been considering taxing all unhealthy foods to tackle childhood obesity.
A report by Professor Dame Sally Davies is due in September and was commissioned by a key ally of Mr Johnson’s, Health Secretary Matt Hancock.
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